Recently, great efforts have been focused on solar evaporators because they can localize solar heat on the air-water interface resulting in enhanced photothermal conversion efficiency. However, to prevent salt accumulation during evaporation while maintaining high evaporation rates is still a challenge. In this work, a salt-rejecting solar evaporator was fabricated for continuous seawater desalination. The evaporator was composed of a top layer of carbon black (CB) nanoparticles for solar absorbance, an interlayer of superhydrophilic melamine formaldehyde (MF) foam for both seawater and concentrated brine delivery, and an outlayer of expandable polyethylene (EPE) foam for floating and heat insulation. The superhydrophilic MF foam could offer a channel for rapid exchange of the concentrated brine with the solution beneath, thereby preventing salt accumulation in the evaporator. It was demonstrated that the salt-rejecting solar evaporator produced a high water evaporation rate of 1.24 kg·m-2·h-1 under 1 kW·m-2 solar irradiance, which was 3.2 times higher than that of the pristine simulated seawater (3.5 wt% NaCl solution). Furthermore, the salt-rejecting evaporator displayed an excellent stability as the water evaporation rate remained constant even after 16-cycles of use within 20 days.